Matta, IbrahimShankar, A. UdayaMultiple-class multiple-resource (MCMR) systems, where a class of customers requires a set of resources, are common. These systems are often analyzed under steady-state conditions. We describe a simple numerical-analytical method, referred to as Z-iteration, to estimate instantaneous (and steady-state) probability measures of time-dependent systems. The key idea is to approximate the relationship between certain instantaneous measures by the relationship between their steady-state counterparts, and use this approximation to solve dynamic flow equations. We show the generality of the Z-iteration by applying it to an integrated communication network, a parallel database server, and a distributed batch system. Validations against exact numerical solutions and discrete-event simulations show the accuracy and computational advantages of the Z-iteration. (Also cross-referenced as UMIACS-TR-94-116.1)en-USTechnical Report